Memory system operations are extended for a data processor by DMA, cache, or memory controller to include a DMA descriptor, including a set of operations and parameters for the operations, which provides for data compression and decompression during or in conjunction with processes for moving data between memory elements of the memory system. The set of operations can be configured to use the parameters and perform the operations of the DMA, cache, or memory controller. The DMA, cache, or memory controller can support moves between memory having a first access latency, such as memory integrated on the same chip as a processor core, and memory having a second access latency that is longer than the first access latency, such as memory on a different integrated circuit than the processor core.